pacman::p_load(olsrr, corrplot, ggpubr, sf, spdep, GWmodel, tmap, tidyverse, gtsummary)Hands-On Exercise 8: Geographically Weighted Regression
Hands-On Exercise
Calibrating Hedonic Pricing Model for Private Highrise Property with GWR Method
1.0 Slides Notes
Regression
- Model the relationships among variables
- Then estimate outcomes from the modelled relationship
Simple Applications
- Do 2-variable linear regression and do least-squares
Assessing Goodness of Fit
- Total sum of squares (TSS)
- Explained sum of squares (ESS)
- Residual sum of squares (RSS)
\(TSS = ESS + RSS\)
\(\sum^n_{i=1}(y_i-\bar{y})^2 = \sum^n_{i=1}(\hat{y}-{\bar{y}})^2 + \sum^n_{i=1}(y_i-\hat{y_i})^2\)
\(R^2\) is the coefficient of determination (Proportion of the total explained variation in y)
Regression Significance Testing
Use the F-Test
Hypothesis: Variation explained by the models is not due to chance
Individual Parameter Testing
null hypothesis is b=0
Test statistic is \(\frac{b_observed - b_expected}{SE_b}\)
Degrees of freedom is \(N-p-1\), where N is total sample size, p is number of predictors
Variable Inflation Factors (VIF)
Variables with high collinearity, these will just add unnecessary variance to the model
Assumption of Linear Regression Models
Linearity assumption: Rel. between dep. and indep. vars is approximately linear
Normality assumption: \(\epsilon\) ~ Normal
Homogeneity of residuals variance: Residuals should have constant variance (Homoscedasticity)
Residuals are uncorrelated with each other (e.g. no serial correlation with time series data)
Optional criteria \(\epsilon ~ N(0, \sigma)\)
Linearity Assumption Confirmation
When plotting the residuals vs fitted values, the fitted line from the plot should be horizontal without distinct patterns
They should not spray everywhere or form curves
Data Transformation
Clarify this slide, what transformation wans applied to linearise the relationship?
Normality Assumption (For the residuals)
The histogram should show a gaussian dist.
Checking for serial correlation
E.g. checking for temporal correlation, make sure that they don’t correlate with time (Show a pattern)
Spatial Non-Stationary
Naive applications of linear regression are assumed to be spatially stationary. Not good for modelling spatial processes
How Relationships Vary Spatially?
Sampling variation
- Nuisance variation: Not actually spatially non-stationary
Relationships intrinsically different across space - The variation is actually dependent on space
Model misspecification
Other Definitions
Spatially non-stationarity: - Same stimulus but different response in different parts of the study region
Global models: - Location independent, spatially stationary
Local models: - Not global, expected from spatial data
Assumption of Spatial Autocorrelation
Goes back to local moran’s
Geographically Weighted Regression (GWR)
LOCAL STATISTICAL TECHNIQUE to analyse spatial variations in relationships
Assumes spatial non-stationarity, will be tested
Follows first law of geography
\(y_i = \beta_0(u_i, v_i) + \sum_k \beta_k(u_i,v_i)x_{ik} + \epsilon_i\)
Where \(u_i, v_i\) are the coordinates of point \(i\) and \(\beta_k(u_i, v_i)\) is the realization of the continuous function at point i
Calibration of GWR
Use local weighted least squares - Give weights based on the locations, following 1st law of geography
Weight examples
Global model: \(w_{ij} = 1\)
Gaussian: \(w_{ij}=exp(-\frac{1}{2}(\frac{d_{ij}}{b})^2)\)
Like different weighting schemes for other locations for a given location. Can be fixed or adaptive
Calibration: Determining Bandwidth
- Least cross-validation score
- Least Akaike Information Criterion (AIC)
Extras
GWR reports should show - Local \(R^2\) - Intercept
2.0 Dependencies
olsrr: OLS and performing diagnostics tests
GWmodel: calibrating geographical weighted family of models
3.0 Wrangling
Load
mpsz = st_read(dsn = "data/geospatial", layer = "MP14_SUBZONE_WEB_PL")Reading layer `MP14_SUBZONE_WEB_PL' from data source
`/Users/matthewho/Work/Y3S2/IS415/Website/IS415/HandsOnEx/HE8/data/geospatial'
using driver `ESRI Shapefile'
Simple feature collection with 323 features and 15 fields
Geometry type: MULTIPOLYGON
Dimension: XY
Bounding box: xmin: 2667.538 ymin: 15748.72 xmax: 56396.44 ymax: 50256.33
Projected CRS: SVY21CRS
mpsz_svy21 <- st_transform(mpsz, 3414)st_bbox
st_bbox(mpsz_svy21) xmin ymin xmax ymax
2667.538 15748.721 56396.440 50256.334 Aspatial Wrangling
condo_resale = read_csv("data/aspatial/Condo_resale_2015.csv")glimpse(condo_resale)Rows: 1,436
Columns: 23
$ LATITUDE <dbl> 1.287145, 1.328698, 1.313727, 1.308563, 1.321437,…
$ LONGITUDE <dbl> 103.7802, 103.8123, 103.7971, 103.8247, 103.9505,…
$ POSTCODE <dbl> 118635, 288420, 267833, 258380, 467169, 466472, 3…
$ SELLING_PRICE <dbl> 3000000, 3880000, 3325000, 4250000, 1400000, 1320…
$ AREA_SQM <dbl> 309, 290, 248, 127, 145, 139, 218, 141, 165, 168,…
$ AGE <dbl> 30, 32, 33, 7, 28, 22, 24, 24, 27, 31, 17, 22, 6,…
$ PROX_CBD <dbl> 7.941259, 6.609797, 6.898000, 4.038861, 11.783402…
$ PROX_CHILDCARE <dbl> 0.16597932, 0.28027246, 0.42922669, 0.39473543, 0…
$ PROX_ELDERLYCARE <dbl> 2.5198118, 1.9333338, 0.5021395, 1.9910316, 1.121…
$ PROX_URA_GROWTH_AREA <dbl> 6.618741, 7.505109, 6.463887, 4.906512, 6.410632,…
$ PROX_HAWKER_MARKET <dbl> 1.76542207, 0.54507614, 0.37789301, 1.68259969, 0…
$ PROX_KINDERGARTEN <dbl> 0.05835552, 0.61592412, 0.14120309, 0.38200076, 0…
$ PROX_MRT <dbl> 0.5607188, 0.6584461, 0.3053433, 0.6910183, 0.528…
$ PROX_PARK <dbl> 1.1710446, 0.1992269, 0.2779886, 0.9832843, 0.116…
$ PROX_PRIMARY_SCH <dbl> 1.6340256, 0.9747834, 1.4715016, 1.4546324, 0.709…
$ PROX_TOP_PRIMARY_SCH <dbl> 3.3273195, 0.9747834, 1.4715016, 2.3006394, 0.709…
$ PROX_SHOPPING_MALL <dbl> 2.2102717, 2.9374279, 1.2256850, 0.3525671, 1.307…
$ PROX_SUPERMARKET <dbl> 0.9103958, 0.5900617, 0.4135583, 0.4162219, 0.581…
$ PROX_BUS_STOP <dbl> 0.10336166, 0.28673408, 0.28504777, 0.29872340, 0…
$ NO_Of_UNITS <dbl> 18, 20, 27, 30, 30, 31, 32, 32, 32, 32, 34, 34, 3…
$ FAMILY_FRIENDLY <dbl> 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0…
$ FREEHOLD <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1…
$ LEASEHOLD_99YR <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…summary(condo_resale) LATITUDE LONGITUDE POSTCODE SELLING_PRICE
Min. :1.240 Min. :103.7 Min. : 18965 Min. : 540000
1st Qu.:1.309 1st Qu.:103.8 1st Qu.:259849 1st Qu.: 1100000
Median :1.328 Median :103.8 Median :469298 Median : 1383222
Mean :1.334 Mean :103.8 Mean :440439 Mean : 1751211
3rd Qu.:1.357 3rd Qu.:103.9 3rd Qu.:589486 3rd Qu.: 1950000
Max. :1.454 Max. :104.0 Max. :828833 Max. :18000000
AREA_SQM AGE PROX_CBD PROX_CHILDCARE
Min. : 34.0 Min. : 0.00 Min. : 0.3869 Min. :0.004927
1st Qu.:103.0 1st Qu.: 5.00 1st Qu.: 5.5574 1st Qu.:0.174481
Median :121.0 Median :11.00 Median : 9.3567 Median :0.258135
Mean :136.5 Mean :12.14 Mean : 9.3254 Mean :0.326313
3rd Qu.:156.0 3rd Qu.:18.00 3rd Qu.:12.6661 3rd Qu.:0.368293
Max. :619.0 Max. :37.00 Max. :19.1804 Max. :3.465726
PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_HAWKER_MARKET PROX_KINDERGARTEN
Min. :0.05451 Min. :0.2145 Min. :0.05182 Min. :0.004927
1st Qu.:0.61254 1st Qu.:3.1643 1st Qu.:0.55245 1st Qu.:0.276345
Median :0.94179 Median :4.6186 Median :0.90842 Median :0.413385
Mean :1.05351 Mean :4.5981 Mean :1.27987 Mean :0.458903
3rd Qu.:1.35122 3rd Qu.:5.7550 3rd Qu.:1.68578 3rd Qu.:0.578474
Max. :3.94916 Max. :9.1554 Max. :5.37435 Max. :2.229045
PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_TOP_PRIMARY_SCH
Min. :0.05278 Min. :0.02906 Min. :0.07711 Min. :0.07711
1st Qu.:0.34646 1st Qu.:0.26211 1st Qu.:0.44024 1st Qu.:1.34451
Median :0.57430 Median :0.39926 Median :0.63505 Median :1.88213
Mean :0.67316 Mean :0.49802 Mean :0.75471 Mean :2.27347
3rd Qu.:0.84844 3rd Qu.:0.65592 3rd Qu.:0.95104 3rd Qu.:2.90954
Max. :3.48037 Max. :2.16105 Max. :3.92899 Max. :6.74819
PROX_SHOPPING_MALL PROX_SUPERMARKET PROX_BUS_STOP NO_Of_UNITS
Min. :0.0000 Min. :0.0000 Min. :0.001595 Min. : 18.0
1st Qu.:0.5258 1st Qu.:0.3695 1st Qu.:0.098356 1st Qu.: 188.8
Median :0.9357 Median :0.5687 Median :0.151710 Median : 360.0
Mean :1.0455 Mean :0.6141 Mean :0.193974 Mean : 409.2
3rd Qu.:1.3994 3rd Qu.:0.7862 3rd Qu.:0.220466 3rd Qu.: 590.0
Max. :3.4774 Max. :2.2441 Max. :2.476639 Max. :1703.0
FAMILY_FRIENDLY FREEHOLD LEASEHOLD_99YR
Min. :0.0000 Min. :0.0000 Min. :0.0000
1st Qu.:0.0000 1st Qu.:0.0000 1st Qu.:0.0000
Median :0.0000 Median :0.0000 Median :0.0000
Mean :0.4868 Mean :0.4227 Mean :0.4882
3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:1.0000
Max. :1.0000 Max. :1.0000 Max. :1.0000 Aspatial to sf
condo_resale.sf <- st_as_sf(condo_resale,
coords = c("LONGITUDE", "LATITUDE"),
crs=4326) %>%
st_transform(crs=3414)head(condo_resale.sf)Simple feature collection with 6 features and 21 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 22085.12 ymin: 29951.54 xmax: 41042.56 ymax: 34546.2
Projected CRS: SVY21 / Singapore TM
# A tibble: 6 × 22
POSTCODE SELLING_PRICE AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE
<dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
1 118635 3000000 309 30 7.94 0.166 2.52
2 288420 3880000 290 32 6.61 0.280 1.93
3 267833 3325000 248 33 6.90 0.429 0.502
4 258380 4250000 127 7 4.04 0.395 1.99
5 467169 1400000 145 28 11.8 0.119 1.12
6 466472 1320000 139 22 10.3 0.125 0.789
# ℹ 15 more variables: PROX_URA_GROWTH_AREA <dbl>, PROX_HAWKER_MARKET <dbl>,
# PROX_KINDERGARTEN <dbl>, PROX_MRT <dbl>, PROX_PARK <dbl>,
# PROX_PRIMARY_SCH <dbl>, PROX_TOP_PRIMARY_SCH <dbl>,
# PROX_SHOPPING_MALL <dbl>, PROX_SUPERMARKET <dbl>, PROX_BUS_STOP <dbl>,
# NO_Of_UNITS <dbl>, FAMILY_FRIENDLY <dbl>, FREEHOLD <dbl>,
# LEASEHOLD_99YR <dbl>, geometry <POINT [m]>4.0 EDA
See dist of SELLING_PRICE
ggplot(data=condo_resale.sf, aes(x=`SELLING_PRICE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
Fix dist. with log
condo_resale.sf <- condo_resale.sf %>%
mutate(`LOG_SELLING_PRICE` = log(SELLING_PRICE))
ggplot(data=condo_resale.sf, aes(x=`LOG_SELLING_PRICE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
Multiple barplot with ggarrange
AREA_SQM <- ggplot(data=condo_resale.sf, aes(x= `AREA_SQM`)) +
geom_histogram(bins=20, color="black", fill="light blue")
AGE <- ggplot(data=condo_resale.sf, aes(x= `AGE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_CBD <- ggplot(data=condo_resale.sf, aes(x= `PROX_CBD`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_CHILDCARE <- ggplot(data=condo_resale.sf, aes(x= `PROX_CHILDCARE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_ELDERLYCARE <- ggplot(data=condo_resale.sf, aes(x= `PROX_ELDERLYCARE`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_URA_GROWTH_AREA <- ggplot(data=condo_resale.sf,
aes(x= `PROX_URA_GROWTH_AREA`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_HAWKER_MARKET <- ggplot(data=condo_resale.sf, aes(x= `PROX_HAWKER_MARKET`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_KINDERGARTEN <- ggplot(data=condo_resale.sf, aes(x= `PROX_KINDERGARTEN`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_MRT <- ggplot(data=condo_resale.sf, aes(x= `PROX_MRT`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_PARK <- ggplot(data=condo_resale.sf, aes(x= `PROX_PARK`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_PRIMARY_SCH <- ggplot(data=condo_resale.sf, aes(x= `PROX_PRIMARY_SCH`)) +
geom_histogram(bins=20, color="black", fill="light blue")
PROX_TOP_PRIMARY_SCH <- ggplot(data=condo_resale.sf,
aes(x= `PROX_TOP_PRIMARY_SCH`)) +
geom_histogram(bins=20, color="black", fill="light blue")
ggarrange(AREA_SQM, AGE, PROX_CBD, PROX_CHILDCARE, PROX_ELDERLYCARE,
PROX_URA_GROWTH_AREA, PROX_HAWKER_MARKET, PROX_KINDERGARTEN, PROX_MRT,
PROX_PARK, PROX_PRIMARY_SCH, PROX_TOP_PRIMARY_SCH,
ncol = 3, nrow = 4)
Statistical point map with tmap
tm_shape(mpsz_svy21)+
tm_polygons() +
tm_shape(condo_resale.sf) +
tm_dots(col = "SELLING_PRICE",
alpha = 0.6,
style="quantile") +
tm_view(set.zoom.limits = c(11,14))
5.0 Hedonic Pricing Modelling in R
Simple Linear Regression Method
condo.slr <- lm(formula=SELLING_PRICE ~ AREA_SQM, data = condo_resale.sf)
summary(condo.slr)
Call:
lm(formula = SELLING_PRICE ~ AREA_SQM, data = condo_resale.sf)
Residuals:
Min 1Q Median 3Q Max
-3695815 -391764 -87517 258900 13503875
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -258121.1 63517.2 -4.064 5.09e-05 ***
AREA_SQM 14719.0 428.1 34.381 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 942700 on 1434 degrees of freedom
Multiple R-squared: 0.4518, Adjusted R-squared: 0.4515
F-statistic: 1182 on 1 and 1434 DF, p-value: < 2.2e-16ggplot(data=condo_resale.sf,
aes(x=`AREA_SQM`, y=`SELLING_PRICE`)) +
geom_point() +
geom_smooth(method = lm)
Multiple Linear Regression Method
Check for multicollinearity issues
corrplot(cor(condo_resale[, 5:23]), diag = FALSE, order = "AOE",
tl.pos = "td", tl.cex = 0.5, method = "number", type = "upper")
Using lm to calibrate the MLR model
condo.mlr <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET + PROX_KINDERGARTEN +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sf)
summary(condo.mlr)
Call:
lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD + PROX_CHILDCARE +
PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_HAWKER_MARKET +
PROX_KINDERGARTEN + PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_TOP_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_SUPERMARKET +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale.sf)
Residuals:
Min 1Q Median 3Q Max
-3475964 -293923 -23069 241043 12260381
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 481728.40 121441.01 3.967 7.65e-05 ***
AREA_SQM 12708.32 369.59 34.385 < 2e-16 ***
AGE -24440.82 2763.16 -8.845 < 2e-16 ***
PROX_CBD -78669.78 6768.97 -11.622 < 2e-16 ***
PROX_CHILDCARE -351617.91 109467.25 -3.212 0.00135 **
PROX_ELDERLYCARE 171029.42 42110.51 4.061 5.14e-05 ***
PROX_URA_GROWTH_AREA 38474.53 12523.57 3.072 0.00217 **
PROX_HAWKER_MARKET 23746.10 29299.76 0.810 0.41782
PROX_KINDERGARTEN 147468.99 82668.87 1.784 0.07466 .
PROX_MRT -314599.68 57947.44 -5.429 6.66e-08 ***
PROX_PARK 563280.50 66551.68 8.464 < 2e-16 ***
PROX_PRIMARY_SCH 180186.08 65237.95 2.762 0.00582 **
PROX_TOP_PRIMARY_SCH 2280.04 20410.43 0.112 0.91107
PROX_SHOPPING_MALL -206604.06 42840.60 -4.823 1.57e-06 ***
PROX_SUPERMARKET -44991.80 77082.64 -0.584 0.55953
PROX_BUS_STOP 683121.35 138353.28 4.938 8.85e-07 ***
NO_Of_UNITS -231.18 89.03 -2.597 0.00951 **
FAMILY_FRIENDLY 140340.77 47020.55 2.985 0.00289 **
FREEHOLD 359913.01 49220.22 7.312 4.38e-13 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 755800 on 1417 degrees of freedom
Multiple R-squared: 0.6518, Adjusted R-squared: 0.6474
F-statistic: 147.4 on 18 and 1417 DF, p-value: < 2.2e-16Removing non-statisically significant variables
condo.mlr1 <- lm(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK +
PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sf)
ols_regress(condo.mlr1) Model Summary
-----------------------------------------------------------------------------
R 0.807 RMSE 751998.679
R-Squared 0.651 MSE 571471422208.592
Adj. R-Squared 0.647 Coef. Var 43.168
Pred R-Squared 0.638 AIC 42966.758
MAE 414819.628 SBC 43051.072
-----------------------------------------------------------------------------
RMSE: Root Mean Square Error
MSE: Mean Square Error
MAE: Mean Absolute Error
AIC: Akaike Information Criteria
SBC: Schwarz Bayesian Criteria
ANOVA
--------------------------------------------------------------------------------
Sum of
Squares DF Mean Square F Sig.
--------------------------------------------------------------------------------
Regression 1.512586e+15 14 1.080418e+14 189.059 0.0000
Residual 8.120609e+14 1421 571471422208.592
Total 2.324647e+15 1435
--------------------------------------------------------------------------------
Parameter Estimates
-----------------------------------------------------------------------------------------------------------------
model Beta Std. Error Std. Beta t Sig lower upper
-----------------------------------------------------------------------------------------------------------------
(Intercept) 527633.222 108183.223 4.877 0.000 315417.244 739849.200
AREA_SQM 12777.523 367.479 0.584 34.771 0.000 12056.663 13498.382
AGE -24687.739 2754.845 -0.167 -8.962 0.000 -30091.739 -19283.740
PROX_CBD -77131.323 5763.125 -0.263 -13.384 0.000 -88436.469 -65826.176
PROX_CHILDCARE -318472.751 107959.512 -0.084 -2.950 0.003 -530249.889 -106695.613
PROX_ELDERLYCARE 185575.623 39901.864 0.090 4.651 0.000 107302.737 263848.510
PROX_URA_GROWTH_AREA 39163.254 11754.829 0.060 3.332 0.001 16104.571 62221.936
PROX_MRT -294745.107 56916.367 -0.112 -5.179 0.000 -406394.234 -183095.980
PROX_PARK 570504.807 65507.029 0.150 8.709 0.000 442003.938 699005.677
PROX_PRIMARY_SCH 159856.136 60234.599 0.062 2.654 0.008 41697.849 278014.424
PROX_SHOPPING_MALL -220947.251 36561.832 -0.115 -6.043 0.000 -292668.213 -149226.288
PROX_BUS_STOP 682482.221 134513.243 0.134 5.074 0.000 418616.359 946348.082
NO_Of_UNITS -245.480 87.947 -0.053 -2.791 0.005 -418.000 -72.961
FAMILY_FRIENDLY 146307.576 46893.021 0.057 3.120 0.002 54320.593 238294.560
FREEHOLD 350599.812 48506.485 0.136 7.228 0.000 255447.802 445751.821
-----------------------------------------------------------------------------------------------------------------Publication quality tables
tbl_regression(condo.mlr1, intercept = TRUE)| Characteristic | Beta | 95% CI1 | p-value |
|---|---|---|---|
| (Intercept) | 527,633 | 315,417, 739,849 | <0.001 |
| AREA_SQM | 12,778 | 12,057, 13,498 | <0.001 |
| AGE | -24,688 | -30,092, -19,284 | <0.001 |
| PROX_CBD | -77,131 | -88,436, -65,826 | <0.001 |
| PROX_CHILDCARE | -318,473 | -530,250, -106,696 | 0.003 |
| PROX_ELDERLYCARE | 185,576 | 107,303, 263,849 | <0.001 |
| PROX_URA_GROWTH_AREA | 39,163 | 16,105, 62,222 | <0.001 |
| PROX_MRT | -294,745 | -406,394, -183,096 | <0.001 |
| PROX_PARK | 570,505 | 442,004, 699,006 | <0.001 |
| PROX_PRIMARY_SCH | 159,856 | 41,698, 278,014 | 0.008 |
| PROX_SHOPPING_MALL | -220,947 | -292,668, -149,226 | <0.001 |
| PROX_BUS_STOP | 682,482 | 418,616, 946,348 | <0.001 |
| NO_Of_UNITS | -245 | -418, -73 | 0.005 |
| FAMILY_FRIENDLY | 146,308 | 54,321, 238,295 | 0.002 |
| FREEHOLD | 350,600 | 255,448, 445,752 | <0.001 |
| 1 CI = Confidence Interval | |||
Same thing for model stats
tbl_regression(condo.mlr1,
intercept = TRUE) %>%
add_glance_source_note(
label = list(sigma ~ "\U03C3"),
include = c(r.squared, adj.r.squared,
AIC, statistic,
p.value, sigma))| Characteristic | Beta | 95% CI1 | p-value |
|---|---|---|---|
| (Intercept) | 527,633 | 315,417, 739,849 | <0.001 |
| AREA_SQM | 12,778 | 12,057, 13,498 | <0.001 |
| AGE | -24,688 | -30,092, -19,284 | <0.001 |
| PROX_CBD | -77,131 | -88,436, -65,826 | <0.001 |
| PROX_CHILDCARE | -318,473 | -530,250, -106,696 | 0.003 |
| PROX_ELDERLYCARE | 185,576 | 107,303, 263,849 | <0.001 |
| PROX_URA_GROWTH_AREA | 39,163 | 16,105, 62,222 | <0.001 |
| PROX_MRT | -294,745 | -406,394, -183,096 | <0.001 |
| PROX_PARK | 570,505 | 442,004, 699,006 | <0.001 |
| PROX_PRIMARY_SCH | 159,856 | 41,698, 278,014 | 0.008 |
| PROX_SHOPPING_MALL | -220,947 | -292,668, -149,226 | <0.001 |
| PROX_BUS_STOP | 682,482 | 418,616, 946,348 | <0.001 |
| NO_Of_UNITS | -245 | -418, -73 | 0.005 |
| FAMILY_FRIENDLY | 146,308 | 54,321, 238,295 | 0.002 |
| FREEHOLD | 350,600 | 255,448, 445,752 | <0.001 |
| R² = 0.651; Adjusted R² = 0.647; AIC = 42,967; Statistic = 189; p-value = <0.001; σ = 755,957 | |||
| 1 CI = Confidence Interval | |||
Multicollinearity check with olsrr: Using ols_vif_tol
ols_vif_tol(condo.mlr1) Variables Tolerance VIF
1 AREA_SQM 0.8728554 1.145665
2 AGE 0.7071275 1.414172
3 PROX_CBD 0.6356147 1.573280
4 PROX_CHILDCARE 0.3066019 3.261559
5 PROX_ELDERLYCARE 0.6598479 1.515501
6 PROX_URA_GROWTH_AREA 0.7510311 1.331503
7 PROX_MRT 0.5236090 1.909822
8 PROX_PARK 0.8279261 1.207837
9 PROX_PRIMARY_SCH 0.4524628 2.210126
10 PROX_SHOPPING_MALL 0.6738795 1.483945
11 PROX_BUS_STOP 0.3514118 2.845664
12 NO_Of_UNITS 0.6901036 1.449058
13 FAMILY_FRIENDLY 0.7244157 1.380423
14 FREEHOLD 0.6931163 1.442759Non-linearity test
ols_plot_resid_fit(condo.mlr1)
Normality assumption test
ols_plot_resid_hist(condo.mlr1)
Normality test: Formal statistical test method
ols_test_normality(condo.mlr1)-----------------------------------------------
Test Statistic pvalue
-----------------------------------------------
Shapiro-Wilk 0.6856 0.0000
Kolmogorov-Smirnov 0.1366 0.0000
Cramer-von Mises 121.0768 0.0000
Anderson-Darling 67.9551 0.0000
-----------------------------------------------Test for spatial autocorrelation
Export the hedonic pricing model as a df
mlr.output <- as.data.frame(condo.mlr1$residuals)Combine w/ sf object
condo_resale.res.sf <- cbind(condo_resale.sf,
condo.mlr1$residuals) %>%
rename(`MLR_RES` = `condo.mlr1.residuals`)Data conversion process
condo_resale.sp <- as_Spatial(condo_resale.res.sf)
condo_resale.spclass : SpatialPointsDataFrame
features : 1436
extent : 14940.85, 43352.45, 24765.67, 48382.81 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 23
names : POSTCODE, SELLING_PRICE, AREA_SQM, AGE, PROX_CBD, PROX_CHILDCARE, PROX_ELDERLYCARE, PROX_URA_GROWTH_AREA, PROX_HAWKER_MARKET, PROX_KINDERGARTEN, PROX_MRT, PROX_PARK, PROX_PRIMARY_SCH, PROX_TOP_PRIMARY_SCH, PROX_SHOPPING_MALL, ...
min values : 18965, 540000, 34, 0, 0.386916393, 0.004927023, 0.054508623, 0.214539508, 0.051817113, 0.004927023, 0.052779424, 0.029064164, 0.077106132, 0.077106132, 0, ...
max values : 828833, 1.8e+07, 619, 37, 19.18042832, 3.46572633, 3.949157205, 9.15540001, 5.374348075, 2.229045366, 3.48037319, 2.16104919, 3.928989144, 6.748192062, 3.477433767, ... Visualise interactive point symbol map
tmap_mode("view")
tm_shape(mpsz_svy21)+
tmap_options(check.and.fix = TRUE) +
tm_polygons(alpha = 0.4) +
tm_shape(condo_resale.res.sf) +
tm_dots(col = "MLR_RES",
alpha = 0.6,
style="quantile") +
tm_view(set.zoom.limits = c(11,14))tmap_mode("plot")Make neighbour and weight matrix for local moran
nb <- dnearneigh(coordinates(condo_resale.sp), 0, 1500, longlat = FALSE)
summary(nb)Neighbour list object:
Number of regions: 1436
Number of nonzero links: 66266
Percentage nonzero weights: 3.213526
Average number of links: 46.14624
10 disjoint connected subgraphs
Link number distribution:
1 3 5 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
3 3 9 4 3 15 10 19 17 45 19 5 14 29 19 6 35 45 18 47
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
16 43 22 26 21 11 9 23 22 13 16 25 21 37 16 18 8 21 4 12
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
8 36 18 14 14 43 11 12 8 13 12 13 4 5 6 12 11 20 29 33
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
15 20 10 14 15 15 11 16 12 10 8 19 12 14 9 8 4 13 11 6
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104
4 9 4 4 4 6 2 16 9 4 5 9 3 9 4 2 1 2 1 1
105 106 107 108 109 110 112 116 125
1 5 9 2 1 3 1 1 1
3 least connected regions:
193 194 277 with 1 link
1 most connected region:
285 with 125 linksnb_lw <- nb2listw(nb, style = 'W')
summary(nb_lw)Characteristics of weights list object:
Neighbour list object:
Number of regions: 1436
Number of nonzero links: 66266
Percentage nonzero weights: 3.213526
Average number of links: 46.14624
10 disjoint connected subgraphs
Link number distribution:
1 3 5 7 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
3 3 9 4 3 15 10 19 17 45 19 5 14 29 19 6 35 45 18 47
25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44
16 43 22 26 21 11 9 23 22 13 16 25 21 37 16 18 8 21 4 12
45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64
8 36 18 14 14 43 11 12 8 13 12 13 4 5 6 12 11 20 29 33
65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84
15 20 10 14 15 15 11 16 12 10 8 19 12 14 9 8 4 13 11 6
85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104
4 9 4 4 4 6 2 16 9 4 5 9 3 9 4 2 1 2 1 1
105 106 107 108 109 110 112 116 125
1 5 9 2 1 3 1 1 1
3 least connected regions:
193 194 277 with 1 link
1 most connected region:
285 with 125 links
Weights style: W
Weights constants summary:
n nn S0 S1 S2
W 1436 2062096 1436 94.81916 5798.341Run the local moran’s test (Another library)
lm.morantest(condo.mlr1, nb_lw)
Global Moran I for regression residuals
data:
model: lm(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA + PROX_MRT +
PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD, data = condo_resale.sf)
weights: nb_lw
Moran I statistic standard deviate = 24.366, p-value < 2.2e-16
alternative hypothesis: greater
sample estimates:
Observed Moran I Expectation Variance
1.438876e-01 -5.487594e-03 3.758259e-05 6.0 Building Hedonic Pricing Models using GWmodel
Fixed bandwidth GWR model
bw.fixed <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS +
FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sp,
approach="CV",
kernel="gaussian",
adaptive=FALSE,
longlat=FALSE)Fixed bandwidth: 17660.96 CV score: 8.259118e+14
Fixed bandwidth: 10917.26 CV score: 7.970454e+14
Fixed bandwidth: 6749.419 CV score: 7.273273e+14
Fixed bandwidth: 4173.553 CV score: 6.300006e+14
Fixed bandwidth: 2581.58 CV score: 5.404958e+14
Fixed bandwidth: 1597.687 CV score: 4.857515e+14
Fixed bandwidth: 989.6077 CV score: 4.722431e+14
Fixed bandwidth: 613.7939 CV score: 1.379526e+16
Fixed bandwidth: 1221.873 CV score: 4.778717e+14
Fixed bandwidth: 846.0596 CV score: 4.791629e+14
Fixed bandwidth: 1078.325 CV score: 4.751406e+14
Fixed bandwidth: 934.7772 CV score: 4.72518e+14
Fixed bandwidth: 1023.495 CV score: 4.730305e+14
Fixed bandwidth: 968.6643 CV score: 4.721317e+14
Fixed bandwidth: 955.7206 CV score: 4.722072e+14
Fixed bandwidth: 976.6639 CV score: 4.721387e+14
Fixed bandwidth: 963.7202 CV score: 4.721484e+14
Fixed bandwidth: 971.7199 CV score: 4.721293e+14
Fixed bandwidth: 973.6083 CV score: 4.721309e+14
Fixed bandwidth: 970.5527 CV score: 4.721295e+14
Fixed bandwidth: 972.4412 CV score: 4.721296e+14
Fixed bandwidth: 971.2741 CV score: 4.721292e+14
Fixed bandwidth: 970.9985 CV score: 4.721293e+14
Fixed bandwidth: 971.4443 CV score: 4.721292e+14
Fixed bandwidth: 971.5496 CV score: 4.721293e+14
Fixed bandwidth: 971.3793 CV score: 4.721292e+14
Fixed bandwidth: 971.3391 CV score: 4.721292e+14
Fixed bandwidth: 971.3143 CV score: 4.721292e+14
Fixed bandwidth: 971.3545 CV score: 4.721292e+14
Fixed bandwidth: 971.3296 CV score: 4.721292e+14
Fixed bandwidth: 971.345 CV score: 4.721292e+14
Fixed bandwidth: 971.3355 CV score: 4.721292e+14
Fixed bandwidth: 971.3413 CV score: 4.721292e+14
Fixed bandwidth: 971.3377 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14
Fixed bandwidth: 971.3405 CV score: 4.721292e+14
Fixed bandwidth: 971.3396 CV score: 4.721292e+14
Fixed bandwidth: 971.3402 CV score: 4.721292e+14
Fixed bandwidth: 971.3398 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14
Fixed bandwidth: 971.3399 CV score: 4.721292e+14
Fixed bandwidth: 971.34 CV score: 4.721292e+14 The result is in metres because the input CRS has metres as the unit, seen in +units=m
condo_resale.spclass : SpatialPointsDataFrame
features : 1436
extent : 14940.85, 43352.45, 24765.67, 48382.81 (xmin, xmax, ymin, ymax)
crs : +proj=tmerc +lat_0=1.36666666666667 +lon_0=103.833333333333 +k=1 +x_0=28001.642 +y_0=38744.572 +ellps=WGS84 +towgs84=0,0,0,0,0,0,0 +units=m +no_defs
variables : 23
names : POSTCODE, SELLING_PRICE, AREA_SQM, AGE, PROX_CBD, PROX_CHILDCARE, PROX_ELDERLYCARE, PROX_URA_GROWTH_AREA, PROX_HAWKER_MARKET, PROX_KINDERGARTEN, PROX_MRT, PROX_PARK, PROX_PRIMARY_SCH, PROX_TOP_PRIMARY_SCH, PROX_SHOPPING_MALL, ...
min values : 18965, 540000, 34, 0, 0.386916393, 0.004927023, 0.054508623, 0.214539508, 0.051817113, 0.004927023, 0.052779424, 0.029064164, 0.077106132, 0.077106132, 0, ...
max values : 828833, 1.8e+07, 619, 37, 19.18042832, 3.46572633, 3.949157205, 9.15540001, 5.374348075, 2.229045366, 3.48037319, 2.16104919, 3.928989144, 6.748192062, 3.477433767, ... Generating the GWR model with the fixed bandwidth and gaussian kernel
gwr.fixed <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH +
PROX_SHOPPING_MALL + PROX_BUS_STOP + NO_Of_UNITS +
FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sp,
bw=bw.fixed,
kernel = 'gaussian',
longlat = FALSE)gwr.fixed ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2024-03-08 21:53:32.940475
Call:
gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale.sp, bw = bw.fixed, kernel = "gaussian",
longlat = FALSE)
Dependent (y) variable: SELLING_PRICE
Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
Number of data points: 1436
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-3470778 -298119 -23481 248917 12234210
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 527633.22 108183.22 4.877 1.20e-06 ***
AREA_SQM 12777.52 367.48 34.771 < 2e-16 ***
AGE -24687.74 2754.84 -8.962 < 2e-16 ***
PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 ***
PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 **
PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 ***
PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 ***
PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 ***
PROX_PARK 570504.81 65507.03 8.709 < 2e-16 ***
PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 **
PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 ***
PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 ***
NO_Of_UNITS -245.48 87.95 -2.791 0.005321 **
FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 **
FREEHOLD 350599.81 48506.48 7.228 7.98e-13 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 756000 on 1421 degrees of freedom
Multiple R-squared: 0.6507
Adjusted R-squared: 0.6472
F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 8.120609e+14
Sigma(hat): 752522.9
AIC: 42966.76
AICc: 42967.14
BIC: 41731.39
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Fixed bandwidth: 971.34
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median 3rd Qu.
Intercept -3.5988e+07 -5.1998e+05 7.6780e+05 1.7412e+06
AREA_SQM 1.0003e+03 5.2758e+03 7.4740e+03 1.2301e+04
AGE -1.3475e+05 -2.0813e+04 -8.6260e+03 -3.7784e+03
PROX_CBD -7.7047e+07 -2.3608e+05 -8.3599e+04 3.4646e+04
PROX_CHILDCARE -6.0097e+06 -3.3667e+05 -9.7426e+04 2.9007e+05
PROX_ELDERLYCARE -3.5001e+06 -1.5970e+05 3.1970e+04 1.9577e+05
PROX_URA_GROWTH_AREA -3.0170e+06 -8.2013e+04 7.0749e+04 2.2612e+05
PROX_MRT -3.5282e+06 -6.5836e+05 -1.8833e+05 3.6922e+04
PROX_PARK -1.2062e+06 -2.1732e+05 3.5383e+04 4.1335e+05
PROX_PRIMARY_SCH -2.2695e+07 -1.7066e+05 4.8472e+04 5.1555e+05
PROX_SHOPPING_MALL -7.2585e+06 -1.6684e+05 -1.0517e+04 1.5923e+05
PROX_BUS_STOP -1.4676e+06 -4.5207e+04 3.7601e+05 1.1664e+06
NO_Of_UNITS -1.3170e+03 -2.4822e+02 -3.0846e+01 2.5496e+02
FAMILY_FRIENDLY -2.2749e+06 -1.1140e+05 7.6214e+03 1.6107e+05
FREEHOLD -9.2067e+06 3.8074e+04 1.5169e+05 3.7528e+05
Max.
Intercept 112794435
AREA_SQM 21575
AGE 434203
PROX_CBD 2704604
PROX_CHILDCARE 1654086
PROX_ELDERLYCARE 38867861
PROX_URA_GROWTH_AREA 78515805
PROX_MRT 3124325
PROX_PARK 18122439
PROX_PRIMARY_SCH 4637517
PROX_SHOPPING_MALL 1529953
PROX_BUS_STOP 11342209
NO_Of_UNITS 12907
FAMILY_FRIENDLY 1720745
FREEHOLD 6073642
************************Diagnostic information*************************
Number of data points: 1436
Effective number of parameters (2trace(S) - trace(S'S)): 438.3807
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 997.6193
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 42263.61
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41632.36
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 42515.71
Residual sum of squares: 2.534069e+14
R-square value: 0.8909912
Adjusted R-square value: 0.8430418
***********************************************************************
Program stops at: 2024-03-08 21:53:33.831642 Building Adaptive Bandwidth GWR Model
Set adaptive to true
bw.adaptive <- bw.gwr(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK +
PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sp,
approach="CV",
kernel="gaussian",
adaptive=TRUE,
longlat=FALSE)Adaptive bandwidth: 895 CV score: 7.952401e+14
Adaptive bandwidth: 561 CV score: 7.667364e+14
Adaptive bandwidth: 354 CV score: 6.953454e+14
Adaptive bandwidth: 226 CV score: 6.15223e+14
Adaptive bandwidth: 147 CV score: 5.674373e+14
Adaptive bandwidth: 98 CV score: 5.426745e+14
Adaptive bandwidth: 68 CV score: 5.168117e+14
Adaptive bandwidth: 49 CV score: 4.859631e+14
Adaptive bandwidth: 37 CV score: 4.646518e+14
Adaptive bandwidth: 30 CV score: 4.422088e+14
Adaptive bandwidth: 25 CV score: 4.430816e+14
Adaptive bandwidth: 32 CV score: 4.505602e+14
Adaptive bandwidth: 27 CV score: 4.462172e+14
Adaptive bandwidth: 30 CV score: 4.422088e+14 Constructing the adaptive bandwidth gwr model
gwr.adaptive <- gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE +
PROX_CBD + PROX_CHILDCARE + PROX_ELDERLYCARE +
PROX_URA_GROWTH_AREA + PROX_MRT + PROX_PARK +
PROX_PRIMARY_SCH + PROX_SHOPPING_MALL + PROX_BUS_STOP +
NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data=condo_resale.sp, bw=bw.adaptive,
kernel = 'gaussian',
adaptive=TRUE,
longlat = FALSE)Showing the model output
gwr.adaptive ***********************************************************************
* Package GWmodel *
***********************************************************************
Program starts at: 2024-03-08 21:53:40.736541
Call:
gwr.basic(formula = SELLING_PRICE ~ AREA_SQM + AGE + PROX_CBD +
PROX_CHILDCARE + PROX_ELDERLYCARE + PROX_URA_GROWTH_AREA +
PROX_MRT + PROX_PARK + PROX_PRIMARY_SCH + PROX_SHOPPING_MALL +
PROX_BUS_STOP + NO_Of_UNITS + FAMILY_FRIENDLY + FREEHOLD,
data = condo_resale.sp, bw = bw.adaptive, kernel = "gaussian",
adaptive = TRUE, longlat = FALSE)
Dependent (y) variable: SELLING_PRICE
Independent variables: AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
Number of data points: 1436
***********************************************************************
* Results of Global Regression *
***********************************************************************
Call:
lm(formula = formula, data = data)
Residuals:
Min 1Q Median 3Q Max
-3470778 -298119 -23481 248917 12234210
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 527633.22 108183.22 4.877 1.20e-06 ***
AREA_SQM 12777.52 367.48 34.771 < 2e-16 ***
AGE -24687.74 2754.84 -8.962 < 2e-16 ***
PROX_CBD -77131.32 5763.12 -13.384 < 2e-16 ***
PROX_CHILDCARE -318472.75 107959.51 -2.950 0.003231 **
PROX_ELDERLYCARE 185575.62 39901.86 4.651 3.61e-06 ***
PROX_URA_GROWTH_AREA 39163.25 11754.83 3.332 0.000885 ***
PROX_MRT -294745.11 56916.37 -5.179 2.56e-07 ***
PROX_PARK 570504.81 65507.03 8.709 < 2e-16 ***
PROX_PRIMARY_SCH 159856.14 60234.60 2.654 0.008046 **
PROX_SHOPPING_MALL -220947.25 36561.83 -6.043 1.93e-09 ***
PROX_BUS_STOP 682482.22 134513.24 5.074 4.42e-07 ***
NO_Of_UNITS -245.48 87.95 -2.791 0.005321 **
FAMILY_FRIENDLY 146307.58 46893.02 3.120 0.001845 **
FREEHOLD 350599.81 48506.48 7.228 7.98e-13 ***
---Significance stars
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 756000 on 1421 degrees of freedom
Multiple R-squared: 0.6507
Adjusted R-squared: 0.6472
F-statistic: 189.1 on 14 and 1421 DF, p-value: < 2.2e-16
***Extra Diagnostic information
Residual sum of squares: 8.120609e+14
Sigma(hat): 752522.9
AIC: 42966.76
AICc: 42967.14
BIC: 41731.39
***********************************************************************
* Results of Geographically Weighted Regression *
***********************************************************************
*********************Model calibration information*********************
Kernel function: gaussian
Adaptive bandwidth: 30 (number of nearest neighbours)
Regression points: the same locations as observations are used.
Distance metric: Euclidean distance metric is used.
****************Summary of GWR coefficient estimates:******************
Min. 1st Qu. Median 3rd Qu.
Intercept -1.3487e+08 -2.4669e+05 7.7928e+05 1.6194e+06
AREA_SQM 3.3188e+03 5.6285e+03 7.7825e+03 1.2738e+04
AGE -9.6746e+04 -2.9288e+04 -1.4043e+04 -5.6119e+03
PROX_CBD -2.5330e+06 -1.6256e+05 -7.7242e+04 2.6624e+03
PROX_CHILDCARE -1.2790e+06 -2.0175e+05 8.7158e+03 3.7778e+05
PROX_ELDERLYCARE -1.6212e+06 -9.2050e+04 6.1029e+04 2.8184e+05
PROX_URA_GROWTH_AREA -7.2686e+06 -3.0350e+04 4.5869e+04 2.4613e+05
PROX_MRT -4.3781e+07 -6.7282e+05 -2.2115e+05 -7.4593e+04
PROX_PARK -2.9020e+06 -1.6782e+05 1.1601e+05 4.6572e+05
PROX_PRIMARY_SCH -8.6418e+05 -1.6627e+05 -7.7853e+03 4.3222e+05
PROX_SHOPPING_MALL -1.8272e+06 -1.3175e+05 -1.4049e+04 1.3799e+05
PROX_BUS_STOP -2.0579e+06 -7.1461e+04 4.1104e+05 1.2071e+06
NO_Of_UNITS -2.1993e+03 -2.3685e+02 -3.4699e+01 1.1657e+02
FAMILY_FRIENDLY -5.9879e+05 -5.0927e+04 2.6173e+04 2.2481e+05
FREEHOLD -1.6340e+05 4.0765e+04 1.9023e+05 3.7960e+05
Max.
Intercept 18758355
AREA_SQM 23064
AGE 13303
PROX_CBD 11346650
PROX_CHILDCARE 2892127
PROX_ELDERLYCARE 2465671
PROX_URA_GROWTH_AREA 7384059
PROX_MRT 1186242
PROX_PARK 2588497
PROX_PRIMARY_SCH 3381462
PROX_SHOPPING_MALL 38038564
PROX_BUS_STOP 12081592
NO_Of_UNITS 1010
FAMILY_FRIENDLY 2072414
FREEHOLD 1813995
************************Diagnostic information*************************
Number of data points: 1436
Effective number of parameters (2trace(S) - trace(S'S)): 350.3088
Effective degrees of freedom (n-2trace(S) + trace(S'S)): 1085.691
AICc (GWR book, Fotheringham, et al. 2002, p. 61, eq 2.33): 41982.22
AIC (GWR book, Fotheringham, et al. 2002,GWR p. 96, eq. 4.22): 41546.74
BIC (GWR book, Fotheringham, et al. 2002,GWR p. 61, eq. 2.34): 41914.08
Residual sum of squares: 2.528227e+14
R-square value: 0.8912425
Adjusted R-square value: 0.8561185
***********************************************************************
Program stops at: 2024-03-08 21:53:41.738645 7.0 Visualising the GWR Output
Terminology - Condition Number: Evaluates local collinearity. If strong local collinearity, result can be unstable. >30 may be unreliable
Local R2: Between 0.0 and 1.0, indicates how well the local regression model fits observed y values. Low values indivate poor performance. Can map the local R2 vals to see where GWR fails, gives clues to missing variables in the model
Predicted: Estimated or fitted y values computed by GWR
Residuals: Should be ~ N(0, 1)
Coefficient standard error: Measures reliability of each coefficient estimate. Higher confidence when standard error are small compared to the actual coefficent values. Large errors can indicate local collinearity issues
Turning SDF into sf dataframe
condo_resale.sf.adaptive <- st_as_sf(gwr.adaptive$SDF) %>%
st_transform(crs=3414)condo_resale.sf.adaptive.svy21 <- st_transform(condo_resale.sf.adaptive, 3414)
condo_resale.sf.adaptive.svy21 Simple feature collection with 1436 features and 51 fields
Geometry type: POINT
Dimension: XY
Bounding box: xmin: 14940.85 ymin: 24765.67 xmax: 43352.45 ymax: 48382.81
Projected CRS: SVY21 / Singapore TM
First 10 features:
Intercept AREA_SQM AGE PROX_CBD PROX_CHILDCARE PROX_ELDERLYCARE
1 2050011.7 9561.892 -9514.634 -120681.9 319266.92 -393417.79
2 1633128.2 16576.853 -58185.479 -149434.2 441102.18 325188.74
3 3433608.2 13091.861 -26707.386 -259397.8 -120116.82 535855.81
4 234358.9 20730.601 -93308.988 2426853.7 480825.28 314783.72
5 2285804.9 6722.836 -17608.018 -316835.5 90764.78 -137384.61
6 -3568877.4 6039.581 -26535.592 327306.1 -152531.19 -700392.85
7 -2874842.4 16843.575 -59166.727 -983577.2 -177810.50 -122384.02
8 2038086.0 6905.135 -17681.897 -285076.6 70259.40 -96012.78
9 1718478.4 9580.703 -14401.128 105803.4 -657698.02 -123276.00
10 3457054.0 14072.011 -31579.884 -234895.4 79961.45 548581.04
PROX_URA_GROWTH_AREA PROX_MRT PROX_PARK PROX_PRIMARY_SCH
1 -159980.20 -299742.96 -172104.47 242668.03
2 -142290.39 -2510522.23 523379.72 1106830.66
3 -253621.21 -936853.28 209099.85 571462.33
4 -2679297.89 -2039479.50 -759153.26 3127477.21
5 303714.81 -44567.05 -10284.62 30413.56
6 -28051.25 733566.47 1511488.92 320878.23
7 1397676.38 -2745430.34 710114.74 1786570.95
8 269368.71 -14552.99 73533.34 53359.73
9 -361974.72 -476785.32 -132067.59 -40128.92
10 -150024.38 -1503835.53 574155.47 108996.67
PROX_SHOPPING_MALL PROX_BUS_STOP NO_Of_UNITS FAMILY_FRIENDLY FREEHOLD
1 300881.390 1210615.4 104.8290640 -9075.370 303955.6
2 -87693.378 1843587.2 -288.3441183 310074.664 396221.3
3 -126732.712 1411924.9 -9.5532945 5949.746 168821.7
4 -29593.342 7225577.5 -161.3551620 1556178.531 1212515.6
5 -7490.586 677577.0 42.2659674 58986.951 328175.2
6 258583.881 1086012.6 -214.3671271 201992.641 471873.1
7 -384251.210 5094060.5 -0.9212521 359659.512 408871.9
8 -39634.902 735767.1 30.1741069 55602.506 347075.0
9 276718.757 2815772.4 675.1615559 -30453.297 503872.8
10 -454726.822 2123557.0 -21.3044311 -100935.586 213324.6
y yhat residual CV_Score Stud_residual Intercept_SE AREA_SQM_SE
1 3000000 2886532 113468.16 0 0.38207013 516105.5 823.2860
2 3880000 3466801 413198.52 0 1.01433140 488083.5 825.2380
3 3325000 3616527 -291527.20 0 -0.83780678 963711.4 988.2240
4 4250000 5435482 -1185481.63 0 -2.84614670 444185.5 617.4007
5 1400000 1388166 11834.26 0 0.03404453 2119620.6 1376.2778
6 1320000 1516702 -196701.95 0 -0.72065801 28572883.7 2348.0091
7 3410000 3266881 143118.77 0 0.41291992 679546.6 893.5893
8 1420000 1431955 -11955.27 0 -0.03033109 2217773.1 1415.2604
9 2025000 1832799 192200.83 0 0.52018109 814281.8 943.8434
10 2550000 2223364 326635.53 0 1.10559735 2410252.0 1271.4073
AGE_SE PROX_CBD_SE PROX_CHILDCARE_SE PROX_ELDERLYCARE_SE
1 5889.782 37411.22 319111.1 120633.34
2 6226.916 23615.06 299705.3 84546.69
3 6510.236 56103.77 349128.5 129687.07
4 6010.511 469337.41 304965.2 127150.69
5 8180.361 410644.47 698720.6 327371.55
6 14601.909 5272846.47 1141599.8 1653002.19
7 8970.629 346164.20 530101.1 148598.71
8 8661.309 438035.69 742532.8 399221.05
9 11791.208 89148.35 704630.7 329683.30
10 9941.980 173532.77 500976.2 281876.74
PROX_URA_GROWTH_AREA_SE PROX_MRT_SE PROX_PARK_SE PROX_PRIMARY_SCH_SE
1 56207.39 185181.3 205499.6 152400.7
2 76956.50 281133.9 229358.7 165150.7
3 95774.60 275483.7 314124.3 196662.6
4 470762.12 279877.1 227249.4 240878.9
5 474339.56 363830.0 364580.9 249087.7
6 5496627.21 730453.2 1741712.0 683265.5
7 371692.97 375511.9 297400.9 344602.8
8 517977.91 423155.4 440984.4 261251.2
9 153436.22 285325.4 304998.4 278258.5
10 239182.57 571355.7 599131.8 331284.8
PROX_SHOPPING_MALL_SE PROX_BUS_STOP_SE NO_Of_UNITS_SE FAMILY_FRIENDLY_SE
1 109268.8 600668.6 218.1258 131474.7
2 98906.8 410222.1 208.9410 114989.1
3 119913.3 464156.7 210.9828 146607.2
4 177104.1 562810.8 361.7767 108726.6
5 301032.9 740922.4 299.5034 160663.7
6 2931208.6 1418333.3 602.5571 331727.0
7 249969.5 821236.4 532.1978 129241.2
8 351634.0 775038.4 338.6777 171895.1
9 289872.7 850095.5 439.9037 220223.4
10 265529.7 631399.2 259.0169 189125.5
FREEHOLD_SE Intercept_TV AREA_SQM_TV AGE_TV PROX_CBD_TV
1 115954.0 3.9720784 11.614302 -1.615447 -3.22582173
2 130110.0 3.3460017 20.087361 -9.344188 -6.32792021
3 141031.5 3.5629010 13.247868 -4.102368 -4.62353528
4 138239.1 0.5276150 33.577223 -15.524302 5.17080808
5 210641.1 1.0784029 4.884795 -2.152474 -0.77155660
6 374347.3 -0.1249043 2.572214 -1.817269 0.06207388
7 182216.9 -4.2305303 18.849348 -6.595605 -2.84136028
8 216649.4 0.9189786 4.879056 -2.041481 -0.65080678
9 220473.7 2.1104224 10.150733 -1.221345 1.18682383
10 206346.2 1.4343123 11.068059 -3.176418 -1.35360852
PROX_CHILDCARE_TV PROX_ELDERLYCARE_TV PROX_URA_GROWTH_AREA_TV PROX_MRT_TV
1 1.00048819 -3.2612693 -2.846248368 -1.61864578
2 1.47178634 3.8462625 -1.848971738 -8.92998600
3 -0.34404755 4.1319138 -2.648105057 -3.40075727
4 1.57665606 2.4756745 -5.691404992 -7.28705261
5 0.12990138 -0.4196596 0.640289855 -0.12249416
6 -0.13361179 -0.4237096 -0.005103357 1.00426206
7 -0.33542751 -0.8235874 3.760298131 -7.31116712
8 0.09462126 -0.2405003 0.520038994 -0.03439159
9 -0.93339393 -0.3739225 -2.359121712 -1.67102293
10 0.15961128 1.9461735 -0.627237944 -2.63204802
PROX_PARK_TV PROX_PRIMARY_SCH_TV PROX_SHOPPING_MALL_TV PROX_BUS_STOP_TV
1 -0.83749312 1.5923022 2.75358842 2.0154464
2 2.28192684 6.7019454 -0.88662640 4.4941192
3 0.66565951 2.9058009 -1.05686949 3.0419145
4 -3.34061770 12.9836105 -0.16709578 12.8383775
5 -0.02820944 0.1220998 -0.02488294 0.9145046
6 0.86781794 0.4696245 0.08821750 0.7656963
7 2.38773567 5.1844351 -1.53719231 6.2029165
8 0.16674816 0.2042469 -0.11271635 0.9493299
9 -0.43301073 -0.1442145 0.95462153 3.3123012
10 0.95831249 0.3290120 -1.71252687 3.3632555
NO_Of_UNITS_TV FAMILY_FRIENDLY_TV FREEHOLD_TV Local_R2
1 0.480589953 -0.06902748 2.621347 0.8846744
2 -1.380026395 2.69655779 3.045280 0.8899773
3 -0.045279967 0.04058290 1.197050 0.8947007
4 -0.446007570 14.31276425 8.771149 0.9073605
5 0.141120178 0.36714544 1.557983 0.9510057
6 -0.355762335 0.60891234 1.260522 0.9247586
7 -0.001731033 2.78285441 2.243875 0.8310458
8 0.089093858 0.32346758 1.602012 0.9463936
9 1.534793921 -0.13828365 2.285410 0.8380365
10 -0.082251138 -0.53369623 1.033819 0.9080753
geometry
1 POINT (22085.12 29951.54)
2 POINT (25656.84 34546.2)
3 POINT (23963.99 32890.8)
4 POINT (27044.28 32319.77)
5 POINT (41042.56 33743.64)
6 POINT (39717.04 32943.1)
7 POINT (28419.1 33513.37)
8 POINT (40763.57 33879.61)
9 POINT (23595.63 28884.78)
10 POINT (24586.56 33194.31)gwr.adaptive.output <- as.data.frame(gwr.adaptive$SDF)
condo_resale.sf.adaptive <- cbind(condo_resale.res.sf, as.matrix(gwr.adaptive.output))glimpse(condo_resale.sf.adaptive)Rows: 1,436
Columns: 77
$ POSTCODE <dbl> 118635, 288420, 267833, 258380, 467169, 466472…
$ SELLING_PRICE <dbl> 3000000, 3880000, 3325000, 4250000, 1400000, 1…
$ AREA_SQM <dbl> 309, 290, 248, 127, 145, 139, 218, 141, 165, 1…
$ AGE <dbl> 30, 32, 33, 7, 28, 22, 24, 24, 27, 31, 17, 22,…
$ PROX_CBD <dbl> 7.941259, 6.609797, 6.898000, 4.038861, 11.783…
$ PROX_CHILDCARE <dbl> 0.16597932, 0.28027246, 0.42922669, 0.39473543…
$ PROX_ELDERLYCARE <dbl> 2.5198118, 1.9333338, 0.5021395, 1.9910316, 1.…
$ PROX_URA_GROWTH_AREA <dbl> 6.618741, 7.505109, 6.463887, 4.906512, 6.4106…
$ PROX_HAWKER_MARKET <dbl> 1.76542207, 0.54507614, 0.37789301, 1.68259969…
$ PROX_KINDERGARTEN <dbl> 0.05835552, 0.61592412, 0.14120309, 0.38200076…
$ PROX_MRT <dbl> 0.5607188, 0.6584461, 0.3053433, 0.6910183, 0.…
$ PROX_PARK <dbl> 1.1710446, 0.1992269, 0.2779886, 0.9832843, 0.…
$ PROX_PRIMARY_SCH <dbl> 1.6340256, 0.9747834, 1.4715016, 1.4546324, 0.…
$ PROX_TOP_PRIMARY_SCH <dbl> 3.3273195, 0.9747834, 1.4715016, 2.3006394, 0.…
$ PROX_SHOPPING_MALL <dbl> 2.2102717, 2.9374279, 1.2256850, 0.3525671, 1.…
$ PROX_SUPERMARKET <dbl> 0.9103958, 0.5900617, 0.4135583, 0.4162219, 0.…
$ PROX_BUS_STOP <dbl> 0.10336166, 0.28673408, 0.28504777, 0.29872340…
$ NO_Of_UNITS <dbl> 18, 20, 27, 30, 30, 31, 32, 32, 32, 32, 34, 34…
$ FAMILY_FRIENDLY <dbl> 0, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 0, 0, 0…
$ FREEHOLD <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1…
$ LEASEHOLD_99YR <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ LOG_SELLING_PRICE <dbl> 14.91412, 15.17135, 15.01698, 15.26243, 14.151…
$ MLR_RES <dbl> -1489099.55, 415494.57, 194129.69, 1088992.71,…
$ Intercept <dbl> 2050011.67, 1633128.24, 3433608.17, 234358.91,…
$ AREA_SQM.1 <dbl> 9561.892, 16576.853, 13091.861, 20730.601, 672…
$ AGE.1 <dbl> -9514.634, -58185.479, -26707.386, -93308.988,…
$ PROX_CBD.1 <dbl> -120681.94, -149434.22, -259397.77, 2426853.66…
$ PROX_CHILDCARE.1 <dbl> 319266.925, 441102.177, -120116.816, 480825.28…
$ PROX_ELDERLYCARE.1 <dbl> -393417.795, 325188.741, 535855.806, 314783.72…
$ PROX_URA_GROWTH_AREA.1 <dbl> -159980.203, -142290.389, -253621.206, -267929…
$ PROX_MRT.1 <dbl> -299742.96, -2510522.23, -936853.28, -2039479.…
$ PROX_PARK.1 <dbl> -172104.47, 523379.72, 209099.85, -759153.26, …
$ PROX_PRIMARY_SCH.1 <dbl> 242668.03, 1106830.66, 571462.33, 3127477.21, …
$ PROX_SHOPPING_MALL.1 <dbl> 300881.390, -87693.378, -126732.712, -29593.34…
$ PROX_BUS_STOP.1 <dbl> 1210615.44, 1843587.22, 1411924.90, 7225577.51…
$ NO_Of_UNITS.1 <dbl> 104.8290640, -288.3441183, -9.5532945, -161.35…
$ FAMILY_FRIENDLY.1 <dbl> -9075.370, 310074.664, 5949.746, 1556178.531, …
$ FREEHOLD.1 <dbl> 303955.61, 396221.27, 168821.75, 1212515.58, 3…
$ y <dbl> 3000000, 3880000, 3325000, 4250000, 1400000, 1…
$ yhat <dbl> 2886531.8, 3466801.5, 3616527.2, 5435481.6, 13…
$ residual <dbl> 113468.16, 413198.52, -291527.20, -1185481.63,…
$ CV_Score <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0…
$ Stud_residual <dbl> 0.38207013, 1.01433140, -0.83780678, -2.846146…
$ Intercept_SE <dbl> 516105.5, 488083.5, 963711.4, 444185.5, 211962…
$ AREA_SQM_SE <dbl> 823.2860, 825.2380, 988.2240, 617.4007, 1376.2…
$ AGE_SE <dbl> 5889.782, 6226.916, 6510.236, 6010.511, 8180.3…
$ PROX_CBD_SE <dbl> 37411.22, 23615.06, 56103.77, 469337.41, 41064…
$ PROX_CHILDCARE_SE <dbl> 319111.1, 299705.3, 349128.5, 304965.2, 698720…
$ PROX_ELDERLYCARE_SE <dbl> 120633.34, 84546.69, 129687.07, 127150.69, 327…
$ PROX_URA_GROWTH_AREA_SE <dbl> 56207.39, 76956.50, 95774.60, 470762.12, 47433…
$ PROX_MRT_SE <dbl> 185181.3, 281133.9, 275483.7, 279877.1, 363830…
$ PROX_PARK_SE <dbl> 205499.6, 229358.7, 314124.3, 227249.4, 364580…
$ PROX_PRIMARY_SCH_SE <dbl> 152400.7, 165150.7, 196662.6, 240878.9, 249087…
$ PROX_SHOPPING_MALL_SE <dbl> 109268.8, 98906.8, 119913.3, 177104.1, 301032.…
$ PROX_BUS_STOP_SE <dbl> 600668.6, 410222.1, 464156.7, 562810.8, 740922…
$ NO_Of_UNITS_SE <dbl> 218.1258, 208.9410, 210.9828, 361.7767, 299.50…
$ FAMILY_FRIENDLY_SE <dbl> 131474.73, 114989.07, 146607.22, 108726.62, 16…
$ FREEHOLD_SE <dbl> 115954.0, 130110.0, 141031.5, 138239.1, 210641…
$ Intercept_TV <dbl> 3.9720784, 3.3460017, 3.5629010, 0.5276150, 1.…
$ AREA_SQM_TV <dbl> 11.614302, 20.087361, 13.247868, 33.577223, 4.…
$ AGE_TV <dbl> -1.6154474, -9.3441881, -4.1023685, -15.524301…
$ PROX_CBD_TV <dbl> -3.22582173, -6.32792021, -4.62353528, 5.17080…
$ PROX_CHILDCARE_TV <dbl> 1.000488185, 1.471786337, -0.344047555, 1.5766…
$ PROX_ELDERLYCARE_TV <dbl> -3.26126929, 3.84626245, 4.13191383, 2.4756745…
$ PROX_URA_GROWTH_AREA_TV <dbl> -2.846248368, -1.848971738, -2.648105057, -5.6…
$ PROX_MRT_TV <dbl> -1.61864578, -8.92998600, -3.40075727, -7.2870…
$ PROX_PARK_TV <dbl> -0.83749312, 2.28192684, 0.66565951, -3.340617…
$ PROX_PRIMARY_SCH_TV <dbl> 1.59230221, 6.70194543, 2.90580089, 12.9836104…
$ PROX_SHOPPING_MALL_TV <dbl> 2.753588422, -0.886626400, -1.056869486, -0.16…
$ PROX_BUS_STOP_TV <dbl> 2.0154464, 4.4941192, 3.0419145, 12.8383775, 0…
$ NO_Of_UNITS_TV <dbl> 0.480589953, -1.380026395, -0.045279967, -0.44…
$ FAMILY_FRIENDLY_TV <dbl> -0.06902748, 2.69655779, 0.04058290, 14.312764…
$ FREEHOLD_TV <dbl> 2.6213469, 3.0452799, 1.1970499, 8.7711485, 1.…
$ Local_R2 <dbl> 0.8846744, 0.8899773, 0.8947007, 0.9073605, 0.…
$ coords.x1 <dbl> 22085.12, 25656.84, 23963.99, 27044.28, 41042.…
$ coords.x2 <dbl> 29951.54, 34546.20, 32890.80, 32319.77, 33743.…
$ geometry <POINT [m]> POINT (22085.12 29951.54), POINT (25656.…summary(gwr.adaptive$SDF$yhat) Min. 1st Qu. Median Mean 3rd Qu. Max.
171347 1102001 1385528 1751842 1982307 13887901 Visualising local R2
tmap_mode("view")
tm_shape(mpsz_svy21)+
tm_polygons(alpha = 0.1) +
tm_shape(condo_resale.sf.adaptive) +
tm_dots(col = "Local_R2",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))tmap_mode("plot")Visualising coefficient estimates
tmap_mode("view")
AREA_SQM_SE <- tm_shape(mpsz_svy21)+
tm_polygons(alpha = 0.1) +
tm_shape(condo_resale.sf.adaptive) +
tm_dots(col = "AREA_SQM_SE",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))
AREA_SQM_TV <- tm_shape(mpsz_svy21)+
tm_polygons(alpha = 0.1) +
tm_shape(condo_resale.sf.adaptive) +
tm_dots(col = "AREA_SQM_TV",
border.col = "gray60",
border.lwd = 1) +
tm_view(set.zoom.limits = c(11,14))
tmap_arrange(AREA_SQM_SE, AREA_SQM_TV,
asp=1, ncol=2,
sync = TRUE)tmap_mode("plot")Limited to URA planning Regions
tm_shape(mpsz_svy21[mpsz_svy21$REGION_N=="CENTRAL REGION", ])+
tm_polygons()+
tm_shape(condo_resale.sf.adaptive) +
tm_bubbles(col = "Local_R2",
size = 0.15,
border.col = "gray60",
border.lwd = 1)